We know no details from the Quran.
The Quran does not mention the name of the son, but from the fact that Isaac is mentioned some verses later, some scholars suggested that it was Ismail who would have been sacrificed. But as this is not explicit, we may also assume that the Quran doesn't stand against the account of the Torah.
According to the Torah (Gen. 22), this event took place after Abraham had sent Hagar and Ismail away.
Before preparing the sacrifice, he left his companions behind and proceeded only with his son Isaac. God and His angel saw it as well.
Thus, there were two humans, Abraham and his son, who knew it and could relate the story. And the angel could tell the story as well.